4 Answers
4

Helicopters are very inefficient in forward flight, for several reasons.

Consider Glauert's high speed assumption, i.e. the helicopter can be represented as an aircraft with a circular wing during high speed flight. Now, if you know anything about basic fixed-wing performance, you'll realize immediately that this implies an aspect ratio just over 1, which is awfully small. You may recall that for a fixed-wing aircraft, induced drag is inversely proportional aspect ratio--so a very low aspect ratio means very high induced drag! Induced drag is normally not a big deal for fixed-wing aircraft at high speed because it's proportional to the square of the lift coefficient (which decreases with speed), but...

In reality, the situation for a helicopter is even worse! Glauert's assumption assumes we have an ideal rotor, i.e. one that has a uniform induced velocity throughout. In practice, the inflow distribution over the rotor is highly non-uniform, especially at high speeds where the advancing side of the rotor is in a very different aerodynamic environment than the retreating side. Even on a very simple level, the "working area" swept on the retreating side is much smaller than that on the advancing side. Since lift needs to be balanced, momentum theory implies a higher induced velocity over the smaller area "worked" by the retreating side, and therefore a much higher induced drag at high speeds than an equivalent fixed wing aircraft.
Rotor wake computation from TsAGI RC-VTOL code (Kritsky, B.S).

As the helicopter goes faster, and as the rotor turns more slowly, more of the retreating side blade will stall, which leads to a dramatic increase in drag. This starts on the inboard section of the blades, and moves outwards as the advance ratio (ratio between flight speed and tip speed) increases. In fact, the most inboard sections of the blade will even be in reversed flow--and airfoils don't work too well backwards.

On the advancing side, things are bad too, but for different reasons. The profile drag of the rotor increases rapidly with speed. Moreover, as the advance ratio increases, the advancing tip Mach number also increases--and as the blades get into the high transonic regime, local shocks begin to form and lead to even larger increases in drag. This can be delayed by slowing the rotor down, but that makes the problems on the retreating side even worse! In general, it's hard to develop airfoils that work well in both regimes.

Outside of the rotor itself, the rotor hub is very draggy, between the main rotor shaft, pitch links, swashplate, hinges and blade grips, etc. Helicopters usually have pretty "utilitarian" fuselages, as well, which are not so well streamlined. Plus, you have the tail rotor, which has most of the same problems as the main rotor.

Back to the specific question of range, the Bregruet range equation says that the range of an aircraft is proportional to the lift-to-drag ratio and the speed of the aircraft. We've already established that the L/D of a helicopter is pretty bad, especially at speed. So, the cruise speed is going to be pretty low and the L/D is going to be pretty low, so to sum up, the range is going to be really low.

The tradeoff is that the helicopter is very good at hovering--even amongst VTOL platforms, the helicopter is the most efficient. Speed and range are the price you pay for that capability.

The rotor blades need to move significantly faster than the craft and therefore incur significantly more drag than fixed wings.

More drag is caused by the suboptimal lift distribution. The centre of the rotor creates little lift because the blades are slow there and is shielded by the fuselage, which causes additional vortices in the middle of the downwash.

The rotor diameter is limited by blade tip speed and material strength, which again limits the efficiency, since it can only affect limited amount of air and has to therefore accelerate it to higher speed, which needs more energy.

Aircraft achieve efficiency by flying high, where the air is thinner and thus drag is lower, and compensate the lower lift by flying faster. But for helicopters it is not possible due to physical limits on the rotor size and speed, nor would it really work, because their induced drag does not decrease so much with speed.

Due to all those limitations, helicopters have relatively less lift for their dry weight and therefore can't take as much fuel.

$\begingroup$I would add that helicopters are not as efficient from the aerodynamic standpoint. The fuselage is always just under the rotor disk, so will be affected by airflow (unless we do away with the cabin ;-)).$\endgroup$
– ALAN WARDJun 23 '15 at 8:07

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$\begingroup$Also: limited fuel tank capacity (2 tons) and more than 10% of the energy lost to power the tail rotor and counter the torque effect created by the main rotor.$\endgroup$
– minsJun 23 '15 at 8:36

$\begingroup$@ALANWARD, well, the fuselage is under the centre of the rotor disk where it produces least lift. But than that is part of the problem. For efficiency it would be best if the rotor produced one nice vortex ring, but that would require the centre to produce most lift and it can't do that.$\endgroup$
– Jan HudecJun 23 '15 at 12:09

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$\begingroup$Helicopters don't fly. They beat the air into submission. This is generally fuel inefficient.$\endgroup$
– PCARRJun 23 '15 at 20:47

Basically, for the same gross mass, a rotorcraft requires considerably more power than a fixed-wing. This is due to the fact that fixed wing aircraft propulsion system needs to create thrust that is equal to the drag of the complete aircraft, and the weight of the aircraft is lifted by the wing-lift force (which is usually 10 or 20 times higher than drag); whereas the rotor of a rotorcraft needs to create thrust that is equal to the total weight of the rotorcraft.

Even if both aircraft have the same engine efficiencies, the helicopter fuel-consumption rate (liters per hour) would be considerably more. So, theoritecally helicopters are not comparable to the efficiency of fixed-wing.

$\begingroup$Where do you get the 10x power/weight figure from? In forward flight, a helicopter isn't that much different than a comparable aircraft--the rotor functions more or less like a wing, albeit a poor one. Looking around for fuel consumption figures, I seem to get ~2x fuel consumption for helicopters compared to comparable prop-driven fixed wing aircraft. See for instance this Aviation.SE question or this thread on the Straight Dope forums.$\endgroup$
– Eric GreenwoodJun 24 '15 at 18:42

$\begingroup$@EricGreenwood, you're right that with forward flight the efficiency of the rotorcraft increases, but still it is 2-3 times less efficient than a comparable fixed wing. I've reworded "10 times" to "considerably more". thanks for pointing out.$\endgroup$
– Gürkan ÇetinJun 26 '15 at 5:20

$\begingroup$Would another factor be that helicopters even if helicopters don't need thrust in excess of their weight all the time, they always need to carry around equipment capable of generating it, while fixed-wing aircraft which aren't designed for combat or acrobatics generally don't?$\endgroup$
– supercatNov 22 '16 at 23:08